A hanging mass M is connected to a four times bigger mass by using a… | JEE Main 2022 (28 Jun, Shift 1)

Q27JEE Main 2022 · 28 JUN · SHIFT 1Medium

Connected Bodies & Pulleys

A hanging mass M is connected to a four times bigger mass by using a string-pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by 2 Mg force. In this situation, tension in the string is $\frac{x}{5}$ Mg for x = ______________. Neglect mass of the string and friction of the block (bigger mass) with ice slab.

(Given g = acceleration due to gravity)

Numerical answer type. Work it out, then open the answer.

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Answer: 6

Net force on the system: $2Mg$ (left, on $4M$ ) minus $Mg$ (weight of hanging $M$ ) $= Mg$ .
$a = \dfrac{Mg}{4M + M} = \dfrac{g}{5}$ ; the hanging mass moves up.
Hanging mass: $T - Mg = M\dfrac{g}{5} \Rightarrow T = \dfrac{6}{5}Mg$
So $x = 6$ .

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